Hundreds of jobs at the Coryton oil refinery in Essex are under threat after Swiss owner Petroplus said it would file for bankruptcy.
The government has said the refinery, which supplies 20% of fuel for south-east England, is still operating.
Administrator PricewaterhouseCoopers says the priority is for work at Coryton to continue without disruption.
Other firms say they will still be able to supply fuel, but petrol retailers fear diesel prices will spike.
Steven Pearson, on behalf of the administrator, said: "Our immediate priority is to continue to operate the Coryton refinery and the Teesside storage business without disruption while the financial position is clarified and restructuring options are explored."
He said there were plans to have a number of discussions during the next few days over the future of the site in Coryton and the business in Teesside.
Petroplus has said it will file for insolvency "as soon as possible" after failing to reach an agreement with creditors to extend deadlines for loan repayments.
'Part of community'
As well as refining oil for use as fuel, the Coryton site - which is one of eight refineries in the UK - also imports fuel from other countries which has already been refined.
Although several lorries left the site before 0730 GMT on Tuesday, there has been no reported movement since.
Russell Jackson, an employee and representative of the Unite union, told the BBC the refinery had been at the site since the 1950s and was very much part of the local community, which would be heartbroken if it closed.
"There are also many contractors that work on site and rely on Coryton for their living as well," he added.
"People don't know what's going to happen and are insecure about the future but people are hopeful something will be done to resolve the situation and a buyer might be found."
He said he hoped the government was concerned about the situation, and warned the UK should not have to solely rely on its energy needs coming from third parties or imports.
East of England MEP Richard Howitt also said he feared petrol supplies would be affected.
He told BBC Radio 5 Live the job losses would have a "devastating impact" on the local economy.
"I don't want to be alarmist about this, but I don't want to be dishonest either.
"Supplies across London and the South East could be affected, and I have been told this could impact the Olympics."
BP is a major customer of the refinery in Coryton, and said it would be watching the situation very closely.
Essar Oil, which owns the Stanlow refinery in Ellesmere Port, has agreed to supply significant volumes of both diesel and petrol to BP, the BBC understands.
Brian Madderson of the Retail Motor Industry (RMI), which represents petrol retailers, told the BBC he expected prices to rise for a number of reasons.
He said the European Union embargo on Iranian supplies of crude oil, the Coryton issues and striking tanker drivers in Lincolnshire were all creating pressure for the industry.
"All of that is going to mean further pressure on price as we have to import for product, and I can see a new record for diesel within days."
The striking Lincolnshire drivers, who work for road haulage firm Wincanton, are in a dispute over pay and conditions.
Unite said the seven-day walkout by 100 of its members, will affect fuel supplies to many Jet garages.
'Financial position'
But discussing the Coryton site, a Department of Energy and Climate Change spokesman said: "We understand that a process is under way to put in place the necessary commercial arrangements to deliver the product into the market.
"Companies have already made alternative arrangements to ensure adequate supply of products are available while these commercial arrangements are being put in place."
There has been very little movement at the refinery since the announcement was made.
ExxonMobil, the owner of the Fawley Refinery on Southampton Water, told the BBC its stock levels for London and the South East remained good and it would continue to deliver to forecourts as normal.
Meanwhile, it has emerged that although Heathrow Airport has one underground pipe taking jet fuel from Coryton, it also has several others it can rely on and therefore is not believed to have any "immediate worries" for now.